Notes on the Rules

The Millennium Prize Problems are hard mathematical problems of considerable interest to the international mathematical community. The publication of a plausible solution to one of them will not go unnoticed, although it may take some years for it to receive general acceptance. The CMI's Scientific Advisory Board (SAB) alone will decide when that point has been reached. The two-year period mentioned in the prize rules is a minimum. It should not be interpreted as a commitment that the SAB will consider a proposed solution after the lapse of two years from publication.

The CMI will not receive or act on direct submissions of proposed solutions, whether or not they have been published, nor will it comment on any material related to the Millennium Prize Prize Problems. In considering a potential solution, the SAB will consider only material that has been published in a refereed mathematics publication of worldwide repute, and that has been in print for at least two years. It will not consider supplementary material submitted by the author of a proposed solution.

A 'refereed publication' is one which receives before publication detailed technical reports on submitted papers or books from independent referees with appropriate expertise and standing in the mathematical community. A journal that allows authors to nominate referees or which simply moderates online postings will not be regarded as a 'refereed publication'. The SAB alone will decide whether a publication is of 'worldwide repute'.

The CMI will not give advice on where proposed solutions should be published.

A paper that does not address or even refer to the specific mathematical questions set out in detail in the official problem description will not be treated as a potential solution of one of the problems, even if it addresses closely related scientific questions.

To be considered for the award of a prize, the author of a proposed solution must have made a major personal contribution to the understanding of the field of the problem in their published solution. A prize will not be awarded to an individual who has simply published the work of another person, or made only small incremental advances on another piece of work.

The 'general acceptance' condition is a positive one. It is not met by default by a paper that has generated little or no reaction since publication. A solution that has been generally accepted will have attracted a large number of citations by independent researchers in the field, will have been the subject of discussion at international meetings, will have received detailed scrutiny in papers by people other than the original authors, and will very likely have been recognised by other awards.